Answer
a. 2.28 percent
b. 38.9 inches
c. .9234
Work Step by Step
a. We find the value of z:
$z=\frac{2.8}{1.4}=2$
Thus, using a table of z-scores, we see that 2.28 percent of men are under 38.8 inches in sitting height.
b. We know that the value of z must be equal to 2.05 so that 98 percent of men are accommodated. Thus, we find:
$h=(1.4)(2.05)+36=39.87 \approx 38.9$
c. We find the value of z:
$z=\frac{1}{(1.4)(.5)}=1.429$
Using an exact value finder given z, we find that this corresponds to a probability of .9234.
